If you want the "fillstyle pattern" to be transparent, just use 'fillstyle transparent pattern N'. Therefore, you should rewrite the “#Q5C_a” part of your script as follows.

#Q5C_a: pattern overlay (full radius, transparent with black lines)

set object 7 circle at 0,0 size 1 arc [angle_c:angle_f] fillstyle transparent pattern 6